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Joanie is making blueberry muffins. The table below shows b, the number of blueberries she used to make m muffins.

Number of Muffins,
m Number of Blueberries,
b
16 144
20 180
24 216
28 252
32 288

If Joanie keeps following this pattern, which of the following equations can she use to find b, the number of blueberries it will take to make m muffins?
A.
m = 9b
B.
b = m + 144
C.
b = 9m
D.
m = b + 144

1 answer

To determine the relationship between the number of muffins \( m \) and the number of blueberries \( b \), let's analyze the data given in the table:

  • For \( m = 16 \), \( b = 144 \)
  • For \( m = 20 \), \( b = 180 \)
  • For \( m = 24 \), \( b = 216 \)
  • For \( m = 28 \), \( b = 252 \)
  • For \( m = 32 \), \( b = 288 \)

First, we can find the pattern between \( m \) and \( b \). Let's calculate the ratio \( \frac{b}{m} \):

  1. For \( m = 16 \): \[ \frac{b}{m} = \frac{144}{16} = 9 \]

  2. For \( m = 20 \): \[ \frac{b}{m} = \frac{180}{20} = 9 \]

  3. For \( m = 24 \): \[ \frac{b}{m} = \frac{216}{24} = 9 \]

  4. For \( m = 28 \): \[ \frac{b}{m} = \frac{252}{28} = 9 \]

  5. For \( m = 32 \): \[ \frac{b}{m} = \frac{288}{32} = 9 \]

From the calculations, we see that the ratio \( \frac{b}{m} = 9 \) holds true.

This indicates that the relationship can be expressed as: \[ b = 9m \]

Now, looking at the provided options, the equation that correctly represents this relationship is:

C. \( b = 9m \)

Thus, the correct answer is C.